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Theory of Thermodynamic Measurements of Quantum Systems Far from Equilibrium

  • Abhay Shastry
Book

Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Abhay Shastry
    Pages 1-11
  3. Abhay Shastry
    Pages 13-42
  4. Abhay Shastry
    Pages 43-59
  5. Abhay Shastry
    Pages 61-75
  6. Abhay Shastry
    Pages 77-114
  7. Abhay Shastry
    Pages 115-117
  8. Back Matter
    Pages 119-144

About this book

Introduction

This thesis presents several related advances in the field of nonequilibrium quantum thermodynamics. The central result is an ingenious proof that the local temperature and voltage measurement in a nonequilibrium system of fermions exists and is unique, placing the concept of local temperature on a rigorous mathematical footing for the first time. As an intermediate step, a proof of the positivity of the Onsager matrix of linear response theory is given -- a statement of the second law of thermodynamics that had lacked an independent proof for 85 years. A new experimental method to measure the local temperature of an electron system using purely electrical techniques is also proposed, which could enable improvements to the spatial resolution of thermometry by several orders of magnitude. Finally, a new mathematically-exact definition for the local entropy of a quantum system in a nonequilibrium steady state is derived. Several different measures of the local entropy are discussed, relating to the thermodynamics of processes that a local observer with varying degrees of information about the microstates of the system could carry out, and it is shown that they satisfy a hierarchy of inequalities. Proofs of the third law of thermodynamics for generic open quantum systems are presented, taking into account the entropic contribution due to localized states. Appropriately normalized (per-state) local entropies are defined and are used to quantify the departure from local equilibrium.

Keywords

nonequilibrium quantum thermodynamics Onsager matrix second law of thermodynamics local entropy in quantum system temperature in quantum system voltage in quantum system scanning probe microscopy temperature outside equilibrium

Authors and affiliations

  • Abhay Shastry
    • 1
  1. 1.Department of ChemistryUniversity of TorontoTorontoCanada

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